The idea of conjugate points, in other word geodesic convergence, is needed for the proof of the singularity theorems.
Jacobi field is what we defined as 
in section 
We cannot show exactly where the conjugate point is. Just place a bound on where it can be.
This can be proved easily. From the Raychaudhuri equation we have :
where we used the fact that 
and 
for geodesics.
As all terms are negative (
everywhere), we have the inequality
from which you find, by integration,
So 
will become infinite, there will be a conjugate point between 
and 
.
An important feature about conjugate points is that you cannot continue through them! It is an end for the geodesics.
